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Importance sampling for multiscale diffusions. (English) Zbl 1250.60031

Summary: We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes, there are additional complications, and, indeed, the straightforward adaptation of importance sampling methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach, we construct schemes and identify conditions under which the schemes are asymptotically optimal. Examples and simulation results are provided.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60F05 Central limit and other weak theorems
60F10 Large deviations
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
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